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Kernel Smoothing Regression

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Kernel Smoothing Regression

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13 Mar 2008 (Updated )

A non-parametrical regression (smoothing) tool using Gaussian kernel.

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Description

Non-parametric regression is widely used in many scientific and engineering areas, such as image processing and pattern recognition.

Non-parametric regression is about to estimate the conditional expectation of a random variable:

E(Y|X) = f(X)

where f is a non-parametric function.

Based on the kernel density estimation technique, this code implements the so called Nadaraya-Watson kernel regression algorithm particularly using the Gaussian kernel. The default bandwidth of the regression is derived from the optimal bendwidth of the Gaussian kernel density estimation suggested in the literature. The code can also take care of missing data.

Acknowledgements

Update Pdf Estimation inspired this file.

This file inspired Plot Some Paths, 3 D Plot For Greeks, Volatility Surface, Coin And Dice, Brain Teaser Solver, Foreign Exchange Options, Log Uniform Jump Diffusion Model, Kernel Regression With Variable Window Width, Multivariant Kernel Regression And Smoothing, and Local Linear Kernel Regression.

MATLAB release MATLAB 7.5 (R2007b)
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Comments and Ratings (18)
09 Mar 2014 cyril

Does it work for multidimensional input x?

23 Sep 2013 KARINA

quisiera saber si existe un algoritmo para hallar el ancho de banda "h"'

15 Mar 2012 temp  
18 Jul 2011 Charles  
08 Jul 2011 ben salah

nice

27 Aug 2009 cf 

It works very well and friendly.

05 Apr 2009 V. Poor  
31 Mar 2009 Michael Jordan  
25 Mar 2009 Kenneth Eaton  
25 Mar 2009 John D'Errico  
25 Mar 2009 Xu Wings  
17 Mar 2009 Gholamreza (Ĺ ahab) Anbarjafari

Hi, nice work :)

21 Dec 2008 Yi Cao

Thanks for the comment. However, the zero median either in X or in Y should not be consider because we deal with a regression problem here. The case mentioned just means that X or Y are constant, then the regrassion problem is not well-posed and the solution is meaningless anyway.

19 Dec 2008 J. Melon

Hi Yi, wouldn't this function produce all NaN if the median of either X or Y is zero? (since h would be zero)

Is there anyway to fix it? for example, if sigma is zero, then let sigma = max(X) - min(X)

17 Nov 2008 Abel Brown

this function rocks!! worked very well 'right outta the box'. My only question: Is is possible to do a variable bandwidth smoothing using this function?

At any rate, nice work
Thanks!

13 Mar 2008 Yi Cao

Dimitri,

Thanks for your suggestions. The file has been updated to take some of your points: typos have been corrected (I hope I found all of them. BTW, I wish the MATLAB editor has a spelling check functionality. -:) ) and valid inputs have been properly checked.

In terms of better bandwidth, I do not aware any simple one available for such problem. Most I knew either too complcated or requires significant computation, such as the one through cross validation. If anyone know this, please leave a message here.

Option for user provided function handle is not implemented. Mainly, I am concerned the difficulty to check the correctness of the function specified (i.e. positiveness and integrating to 1).

Finally, local polynomial regression will require more work. It will be considered in a future version.

13 Mar 2008 Dimitri Shvorob

Oops, I meant 'local polynomial (e.g. local linear) vs. local constant'. Does that make sense? Someone needs to refresh his stats :)

13 Mar 2008 Dimitri Shvorob

Nice work! There are some typos that can be corrected; with more time on their hands, one could add clarification/input check 'x must be a vector', allow an arbitrary set of evaluation points x, make chosen default bandwidth selection procedure more prominent (I have to say I didn't know this one; have you consulted Pagan's little book?), or allow an arbitrary kernel via a function-handle input argument. Do you want to try coding local polynomial (vs. local linear) kernel regression? :)

Updates
24 Dec 2008

add an error case

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